This research applies novel nonlinear signal detection techniques in studies of human subjects with respiratory and cardiac diseases. One of the studies concerns a breathing disorder during sleep, a disease called Obstructive Sleep Apnea (OSA). In a second study we investigate a disease of the heart, Atrial Fibrillation (AF). The former study involves nonlinear processing of the time sequences of sleep apnea recordings (cardio-respirograms) collected from patients with known obstructive sleep apnea, and from a normal control. In the latter study, we apply similar nonlinear metrics to Doppler flow measurements obtained by transesophageal echocardiography (TEE). One of our metrics, the 'chaotic radius' is used for tracking the position of points in phase space relative to some reference position. A second metric, the 'differential radius' provides a measure of the separation rate of contiguous (evolving) points in phase space. A third metric, the 'chaotic frequency' gives angular position of the phase space orbit as a function of time. All are useful for identifying change of physiologic condition that is not always apparent using conventional methods.